Let \(v\in n\)  be a nonzero vector. Write \(v_1 / \Vert v\Vert  = r e^{i \theta }\) , where \(r\)  is a nonnegative real number. (When \(v_1 = 0\) , we have \(r = 0\)  and set \(\theta =0\) .) We define a unitary reflector [1]} as
\(H(v) = (-e^{-i \theta }) \Big [I_n - \frac{(v/\Vert v\Vert  + e^{i \theta } e_1)(v/\Vert v\Vert  + e^{i \theta } e_1)^\ast }{1+r}\Big ].\) 
